In real rotating chiral superfluid \(^3\) He-A, the vortex lattice is created by quenching the critical rotation velocity whereby many different vortex lattices form quasi-equilibrium thermal states, with barriers exceeding 5 order of magnitudes compared to \(T\) . It is therefore expected that the anomaly can be “transferred" between the \(\hat{{l}}\) -vector, \({v}_s\)  and \({v}_n\)  components of the superfluid and this choice is not gauge independent. It would be interesting to study this non-relativistic problem from the geometrical perspective. There is no particular hydrodynamical reason to restrict to low angular velocities, temperatures (compared to \(T_c\) ), chemical potentials, where relativistically, to higher orders [1]}, [2]}

J5 = (242+T212 + 2482 - R962) + ...
with \(R\)  the scalar curvature in the plane perpendicular to \({\Omega }\) . Even better, the higher-order terms should be worked out in detail in terms of the full non-relativistic geometry and compared to the low-energy (relativistic) results and the regime of validity of the chiral transport with Weyl fermions, including torsion [3]}. The ensuing effective hydrodynamic actions for the Goldstones should be worked out in detail.
